1. Field of the Invention
The present application generally relates to generating simulated-diffraction signals/signals for periodic gratings. More particularly, the present application relates to generating a library of simulated-diffraction signals indicative of electromagnetic signals diffracting from periodic gratings.
2. Description of the Related Art
In semiconductor manufacturing, periodic gratings are typically used for quality assurance. For example, one typical use of periodic gratings includes fabricating a periodic grating in proximity to the operating structure of a semiconductor chip. The periodic grating is then illuminated with an electromagnetic radiation. The electromagnetic radiation that deflects off of the periodic grating are collected as a diffraction signal. The diffraction signal is then analyzed to determine whether the periodic grating, and by extension whether the operating structure of the semiconductor chip, has been fabricated according to specifications.
In one conventional system, the diffraction signal collected from illuminating the periodic grating (the measured-diffraction signal) is compared to a library of simulated-diffraction signals. Each simulated-diffraction signal in the library is associated with a theoretical profile. When a match is made between the measured-diffraction signal and one of the simulated-diffraction signals in the library, the theoretical profile associated with the simulated-diffraction signal is presumed to represent the actual profile of the periodic grating.
The accuracy of this conventional system depends, in part, on the range and/or resolution of the library. More particularly, the range of the library relates to the range of different simulated-diffraction signals in the library. As such, if the collected-diffraction signal is outside of the range of the library, then a match cannot be made. The resolution of the library relates to the amount of variance between the different simulated-diffraction signals in the library. As such, a lower resolution produces a coarser match.
Therefore, the accuracy of this convention system can be increased by increasing the range and/or resolution of the library. However, increasing the range and/or the resolution of the library also increases the amount of computations required to generate the library. As such, it is desirable to determine an appropriate range and/or resolution for the library without unduly increasing the amount of computations required.